1. Rene Descartes is a famous mathematician that studied in various different areas of math. He studied at the universeity of Frankeker. Some of his mathematical contributions were rationalism, law of refraction, Cartesia dualism and more.
2. One of his most important contributions was the Cartesia Coordination System. I think this because it specifies yeah point on the coordinate plane making it easier to read. You can use this to specify and point on the plane.
3.Some things that i found interesting about Maria Agnesi is that by the age of 5 she could speak Italian and Freanch and many others at the age of 13. Also that she was the oldest of 21 kids.
4.In 8.1 something that i found was useful was the distance formula. This formula could be used in everyday life. It could help you find out how long you have gone or need to go.
5. The slope intercept form is y=mx+b.
y-4=(1/2)(x-2)
y-4=1/2x+1
y=-1/2x+3
4/29/2011
1. i think that Johann Kepler was more of a scientist. I think this because he study more scientific things such as astronomy, and astrology. Also he invented many things pertaining to science. some of the things he invented were eponymous laws of planetary motion, he invented an improved a version of the refracting telescope, and mysterium cosmographicium which is a book written by Johann Kepler. Conic sections were found used by Johann Kepler in 1609 when he derived his first law of planetary motion. A planet travels in an ellipse with the sun in one focus. Some of Johann Keplers contributions were the laws of planetary motion and the telescope. I think that they are very useful today, because they are used to determind the rotation of planets and their orbits and they are also used for the support for future discoveries.
2.one way that you can uses a logarithm in the real world is in the field of engineering. For example say that the engineer wants to graph the lift of a wing, and wants to show everything up to a jumbo plane. They would use a logarithm to graph it. another example would be to define a pH solution. A third example would be measuring decibles of sound.
3.A problem that i had trouble with in chapter 8 was equation of a circle.For example (-1,2) with a radius of 4. Let h =-1,k =2 and r =4. [x-(-1)]^2 +(y-2)^2 = 4^2
(x+1)^2+(y-2)^2=16
4. the two equations would be :
2x+y=2
x+2y=5
step 1. multiply by -2
(-2)2x+y=2 now you have -4x-2y=-4
step 2. add the two equations
-4x-2y=-4
x+2y=5
-3x=-9 therefore x-3
(3,-4)
5. if i were to explain to a student how to solve system of linear inequalities if would first start like this :
1. write the equation in standard form, ax=by=c
2.multiply the coefficients by there opposites that way you get zero.
3.add the new equation to eliminate a variable.
4. now solve that equation and substitute that result into the other equation and solve for the other variable.
5.check the solution
5/13/2011
1.the Greeks attitude towards mathematics was that it was more abstract in geometry and even though their work was nice it wasnt of much importance. The Greeks didnt think that constructions could be drawn with practical instrument like a ruler. the only tools they used were compasses and a true straight edge. the straigth edge did resemble a ruler the premitted to line up points by eye. the 3 famous antiquitys were to trisect anarbitray angle, to construct the length of the edge of a cube having twice the volume of a given cube, and to construct a square having the same area as that of a given circle. my areas of intrest is how the Greeks came up with constructions and how they figured out that a compass could construct angles and lines and others.
2. some shapes that are used in the real word are squares for windows, circles for tires, octagons for stop signs, rectangles for doors, and a pentagon for the building in Washington DC called the pentagon.
3.Some of Elucids contributions to math were that he wrote the book of elements which is a collection of definitions, postulates, propositions and constructions, and mathematical proofs of the propositions. this is important to mathematic because it covers a wide variety of of mathematical context.
4.A parallelogram is a quadrilatral. A rhombus is a parallelogram because it has 2 pair of sides that run parallel with each other. but not all of the sides are equal. if everything was equal it would be a parallelogram.
2. One of his most important contributions was the Cartesia Coordination System. I think this because it specifies yeah point on the coordinate plane making it easier to read. You can use this to specify and point on the plane.
3.Some things that i found interesting about Maria Agnesi is that by the age of 5 she could speak Italian and Freanch and many others at the age of 13. Also that she was the oldest of 21 kids.
4.In 8.1 something that i found was useful was the distance formula. This formula could be used in everyday life. It could help you find out how long you have gone or need to go.
5. The slope intercept form is y=mx+b.
y-4=(1/2)(x-2)
y-4=1/2x+1
y=-1/2x+3
4/29/2011
1. i think that Johann Kepler was more of a scientist. I think this because he study more scientific things such as astronomy, and astrology. Also he invented many things pertaining to science. some of the things he invented were eponymous laws of planetary motion, he invented an improved a version of the refracting telescope, and mysterium cosmographicium which is a book written by Johann Kepler. Conic sections were found used by Johann Kepler in 1609 when he derived his first law of planetary motion. A planet travels in an ellipse with the sun in one focus. Some of Johann Keplers contributions were the laws of planetary motion and the telescope. I think that they are very useful today, because they are used to determind the rotation of planets and their orbits and they are also used for the support for future discoveries.
2.one way that you can uses a logarithm in the real world is in the field of engineering. For example say that the engineer wants to graph the lift of a wing, and wants to show everything up to a jumbo plane. They would use a logarithm to graph it. another example would be to define a pH solution. A third example would be measuring decibles of sound.
3.A problem that i had trouble with in chapter 8 was equation of a circle.For example (-1,2) with a radius of 4. Let h =-1,k =2 and r =4. [x-(-1)]^2 +(y-2)^2 = 4^2
(x+1)^2+(y-2)^2=16
4. the two equations would be :
2x+y=2
x+2y=5
step 1. multiply by -2
(-2)2x+y=2 now you have -4x-2y=-4
step 2. add the two equations
-4x-2y=-4
x+2y=5
-3x=-9 therefore x-3
(3,-4)
5. if i were to explain to a student how to solve system of linear inequalities if would first start like this :
1. write the equation in standard form, ax=by=c
2.multiply the coefficients by there opposites that way you get zero.
3.add the new equation to eliminate a variable.
4. now solve that equation and substitute that result into the other equation and solve for the other variable.
5.check the solution
5/13/2011
1.the Greeks attitude towards mathematics was that it was more abstract in geometry and even though their work was nice it wasnt of much importance. The Greeks didnt think that constructions could be drawn with practical instrument like a ruler. the only tools they used were compasses and a true straight edge. the straigth edge did resemble a ruler the premitted to line up points by eye. the 3 famous antiquitys were to trisect anarbitray angle, to construct the length of the edge of a cube having twice the volume of a given cube, and to construct a square having the same area as that of a given circle. my areas of intrest is how the Greeks came up with constructions and how they figured out that a compass could construct angles and lines and others.
2. some shapes that are used in the real word are squares for windows, circles for tires, octagons for stop signs, rectangles for doors, and a pentagon for the building in Washington DC called the pentagon.
3.Some of Elucids contributions to math were that he wrote the book of elements which is a collection of definitions, postulates, propositions and constructions, and mathematical proofs of the propositions. this is important to mathematic because it covers a wide variety of of mathematical context.
4.A parallelogram is a quadrilatral. A rhombus is a parallelogram because it has 2 pair of sides that run parallel with each other. but not all of the sides are equal. if everything was equal it would be a parallelogram.